Robust Quickest Correlation Change Detection in High-Dimensional Random Vectors

Abstract: Detecting changes in high-dimensional vectors presents significant challenges, especially when the post-change distribution is unknown and time-varying. This paper introduces a novel robust algorithm for correlation change detection in high-dimensional data. The approach utilizes the summary statistic of the maximum magnitude correlation coefficient to detect the change. This summary statistic captures the level of correlation present in the data but also has an asymptotic density. The robust test is designed using the asymptotic density. The proposed approach is robust because it can help detect a change in correlation level from some known level to unknown, time-varying levels. The proposed test is also computationally efficient and valid for a broad class of data distributions. The effectiveness of the proposed algorithm is demonstrated on simulated data.